Well with Bitcoin anyone can trace you with proper chain analysis tools. This chain analysis industry is getting bigger now a days.
I don't think they can trace IP address. But if you had for example a KYC'ed account on an exchange and you withdraw from it and as an example let's say authorities want to follow your BTC footprint then they can see on what address that BTC went - because all the transactions are linked in the block"chain". However if you ask a person to send BTC in an empty address nobody could theoretically know that is your address.
This is sadly true. The KYC stuff has spoilt the anonymity of what Satoshi initially set out to do. Without a KYC, it's really difficult to trace a transaction to anyone physically. But that's the reality of the time we live in now.